Conceptual models of the climate : 2003 program of study, Non-Newtonian geophysical fluid dynamics

Non-Newtonian fluids occur commonly in our world. These fluids, such as toothpaste, saliva, oils, mud and lava, exhibit a number of behaviors that are different from Newtonian fluids and have a number of additional material properties. In general, these differences arise because the fluid has a microstructure that influences the flow. In section 2 we will present a collection of some of the interesting phenomena arising from flow nonlinearities, the inhibition of stretching, elastic effects and normal stresses. In section 3 we will discuss a variety of devices for measuring material properties, a process known as rheometry.Funding was provided by the Office of Naval Research under Contract No. N00014-97-1-0934 and The National Science Foundation under Contract No. OCE 98-10647

2010 program of study : swirling and swimming in turbulence

Swirling and Swimming in Turbulence was the theme at the 2010 GFD Program. Professors Glenn Flierl (M.I.T.), Antonello Provenzale (ISAC-CNR, Turin) and Jean-Luc Thiffeault (University of Wisconsin) were the principal lecturers. Together they navigated an elegant path through topics ranging from mixing protocols and efficiencies to ecological strategies, schooling and genetic development. The first ten chapters of this volume document these lectures, each prepared by pairs of this summer’s GFD fellows. Following on are the written reports of the fellows’ own research projects.Funding was provided by the Office of Naval Research under Contract No. N000-14-09-10844 and the National Science Foundation through Grant No. OCE 082463

Viscoplastic plates

An asymptotic model is constructed to describe the bending of thin sheets, or plates, of viscoplastic fluid described by the Herschel–Bulkley constitutive law, which incorporates the von Mises yield condition and a nonlinear viscous stress. The model reduces to a number of previous ones from plasticity theory and viscous fluid mechanics in various limits. It is characterized by a yield criterion proposed by Ilyushin which compactly combines the effect of the bending moment and in-plane stress tensors through three particular invariants. The model is used to explore the bending of loaded flat plates, the deflection of impulsively driven circular plates, and the tension-controlled deflection of loaded beams

2004 program of study : tides

The summer of 2004 saw the GFD program tackle “Tides”. Myrl Hendershott (Scripps Institution of Oceanography) gave a fabulous introduction to the subject in the first week of the course, laying the foundations from astronomy and classical geophysical fluid dynamics. In the second week, Chris Garrett (University of Victoria) admirably followed up with recent developments on the subject, including the recent observations from satellite altimetry, their implications to mixing and circulation, and even a memorable lecture on the noble theme of how we might solve the world's energy crisis. The principal lectures proved unusually popular this summer, and the seminar room at Walsh often overflowed in the first two weeks. Following on from the lectures, the seminar schedule of the summer covered in greater detail the oceanographic issues with which researchers are actively grappling. We also heard about related problems regarding atmospheric, planetary and stellar tides, together with the usual mix of topics on GFD in general. The summer once again featured a lecture for the general public in the Woods Hole area. Carl Wunsch delivered a very well received lecture entitled “Climate Change Stories”, in which he gave an impression of how scientists generally believe our climate is currently changing, whilst simultaneously urging caution against some of the more outrageous and exaggerated claims. The lecture was held at Lilly Auditorium, thanks to the hospitality of the Marine Biology Laboratory. The reception following the lecture was enjoyed by all. Neil Balmforth and Stefan Llewellyn Smith acted as Co-Directors for the summer. Janet Fields, Jeanne Fleming and Penny Foster provided the administrative backbone to the Program, both during the summer and throughout the year beforehand. As always, we were grateful to the Woods Hole Oceanographic Institution for the use of Walsh Cottage, and Keith Bradley's solid service could not be overlooked. Shilpa Ghadge and Shreyas Mandre are to be thanked for their part in comforting the fellows, developing the summer's proceedings volume (available on the GFD web site) and for running the computer network.Funding was provided by the Office of Naval Research under Contract No. N00014-04-1-0157 and the National Science Foundation under Grant No. OCE-0325296

Conceptual models of the climate : 2001 program of studies in geophysical fluid dynamics

In 2001, the Geophysical Fluid Dynamics Summer Study Program grappled with Conceptual Models of the Climate. Eli Tziperman (Weizman Institute), Paola Cessi (Scripps Institution of Oceanography) and Ray Pierre- Humbert (University of Chicago) provided the principal lectures. This introduction gave us all a glimpse into the complex problem of the climate, both in the present, past and future, and even on other planets. As always, the next weeks of the program were filled with many seminars from the visitors, and culminated in the fellow's reports

Viscoplastic rimming flow instead a rotating cylinder

A theoretical analysis is presented for the flow of a Herschel-Bulkley fluid around the inside surface of a rotating cylinder, at rotation speeds for which the fluid largely collects in a prominent pool in the lower part of the cylinder. The analysis, based on lubrication theory, predicts the steady states typically reached after a small mumber of rotations. The analysis is also modified to consider the drainage of the film around a stationary cylinder, which allows an exploration of the dynamics when a rotating drum is suddenly stopped. The predictions of the theory are compared with experiments in which a Carbopol suspension is rotated inside an acrylic drum

The Bingham-Rayleigh-Bénard problem

Abstract The development of thermal convection is studied theoretically for a viscoplastic fluid. If the fluid has finite viscosity at zero shear rate, the critical Rayleigh number for convective instability takes the same value as for a Newtonian fluid with that viscosity. The subsequent weakly nonlinear behaviour depends on the degree of shear thinning: with a moderately shear-thinning nonlinear viscosity, the amplitude of convective overturning for a given temperature difference is increased relative to the Newtonian case. If the reduction in viscosity is sufficiently sharp the transition can even become subcritical (a detail particularly relevant to regularized constitutive laws). For a yield-stress fluid, the critical Rayleigh number for linear instability is infinite as the motionless layer is held rigid by the yield stress. Nonlinear convective overturning, however, still occurs and we trace out how the finite-amplitude solution branches develop from their Newtonian counterparts as the yield stress is increased from zero for the Bingham fluid. Preliminary laboratory experiments with a layer of Carbopol fluid heated from below, confirm that yield strength inhibits convection but convection will initiate with a sufficient kick to the system

Visco-plastic models of isothermal lava domes

Author Posting. © Cambridge University Press, 2000. This article is posted here by permission of Cambridge University Press for personal use, not for redistribution. The definitive version was published in Journal of Fluid Mechanics 403 (2000): 37-65, doi:10.1017/S0022112099006916.The dynamics of expanding domes of isothermal lava are studied by treating the lava as a viscoplastic material with the Herschel–Bulkley constitutive law. Thin-layer theory is developed for radially symmetric extrusions onto horizontal plates. This provides an evolution equation for the thickness of the fluid that can be used to model expanding isothermal lava domes. Numerical and analytical solutions are derived that explore the effects of yield stress, shear thinning and basal sliding on the dome evolution. The results are briefly compared with an experimental study. It is found that it is difficult to unravel the combined effects of shear thinning and yield stress; this may prove important to studies that attempt to infer yield stress from morphology of flowing lava.The financial support of an EPSRC Advanced Fellowship is gratefully acknowledged by R.V. C. N. J. B. was partially supported by the NSF Grant OCE-9616017 and an EPSRC Visiting Fellowship Grant GR/M50409